Chemical Equilibrium & ICE Tables practice questions

Question 1

A student injects a sample of colorless $\text{N}_2\text{O}_4\text{(g)}$ into an evacuated, sealed rigid container at a constant temperature. Over time, brown $\text{NO}_2\text{(g)}$ forms according to the reaction $\text{N}_2\text{O}_4\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$. After several minutes, the intensity of the brown color inside the container remains constant. Which of the following best describes the state of the system after the brown color stops changing, and provides the correct justification?

Accepted Answer

The system has reached dynamic equilibrium because the rate of the forward reaction equals the rate of the reverse reaction.

Answer

The reaction has stopped because all of the $\text{N}_2\text{O}_4\text{(g)}$ has been converted into $\text{NO}_2\text{(g)}$.

Answer

The system has reached dynamic equilibrium because the concentration of $\text{N}_2\text{O}_4\text{(g)}$ is equal to the concentration of $\text{NO}_2\text{(g)}$.

Answer

The reaction has stopped because the rates of both the forward and reverse reactions have decreased to zero.

Question 2

A student investigates the industrial synthesis of methane gas from solid carbon and hydrogen gas at high temperatures. The balanced equation for the reversible reaction is shown below.

$\text{C(s)} + 2\,\text{H}_2\text{(g)} \rightleftharpoons \text{CH}_4\text{(g)}$

Which of the following is the correct expression for the equilibrium constant, $K_c$, for this reaction?

Accepted Answer

$K_c = \dfrac{[\text{CH}_4]}{[\text{H}_2]^2}$

Answer

$K_c = \dfrac{[\text{CH}_4]}{[\text{C}][\text{H}_2]^2}$

Answer

$K_c = \dfrac{[\text{CH}_4]}{[\text{H}_2]}$

Answer

$K_c = \dfrac{[\text{H}_2]^2}{[\text{CH}_4]}$

Question 3

Consider the gas-phase reaction represented below, for which $K_c = 5.0 \times 10^{10}$ at $298\text{ K}$:

$$2\text{NO(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$$

Which of the following statements best describes the composition of the mixture at equilibrium at $298\text{ K}$ and provides a correct justification?

Accepted Answer

Products predominate at equilibrium because $K_c \gg 1$, indicating that the equilibrium position strongly favors the products.

Answer

Reactants predominate at equilibrium because a large value of $K_c$ indicates that the reverse reaction is favored.

Answer

Products predominate at equilibrium because the rate of the forward reaction is greater than the rate of the reverse reaction at equilibrium.

Answer

Reactants and products are present in equal concentrations because the rate of the forward reaction equals the rate of the reverse reaction at equilibrium.

Question 4

A gaseous reaction mixture containing $\text{N}_2\text{O}_4\text{(g)}$ and $\text{NO}_2\text{(g)}$ is at equilibrium inside a cylinder fitted with a movable piston at a constant temperature, as represented by the equation $\text{N}_2\text{O}_4\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$. The piston is pushed inward to decrease the volume of the container to half its initial volume. Which of the following best predicts the response of the system to re-establish equilibrium and gives the correct reasoning?

Accepted Answer

The system shifts toward the reactants because decreasing the volume increases the total pressure, favoring the side with fewer moles of gas.

Answer

The system shifts toward the products because decreasing the volume favors the side with a greater number of moles of gas.

Answer

The system shifts toward the products because the value of the equilibrium constant increases when total pressure increases.

Answer

The system shifts toward the reactants because the value of the equilibrium constant decreases when total pressure increases.

Question 5

An aqueous solution contains dihydrogen phosphate ions and ammonia reacting according to the equilibrium below.

$\text{H}_2\text{PO}_4^-\text{(aq)} + \text{NH}_3\text{(aq)} \rightleftharpoons \text{HPO}_4^{2-}\text{(aq)} + \text{NH}_4^+\text{(aq)}$

Which of the following correctly identifies a Brønsted-Lowry acid and its conjugate base in this reaction?

Accepted Answer

Acid: $\text{H}_2\text{PO}_4^-\text{(aq)}$; Conjugate base: $\text{HPO}_4^{2-}\text{(aq)}$

Answer

Acid: $\text{NH}_3\text{(aq)}$; Conjugate base: $\text{NH}_4^+\text{(aq)}$

Answer

Acid: $\text{H}_2\text{PO}_4^-\text{(aq)}$; Conjugate base: $\text{NH}_4^+\text{(aq)}$

Answer

Acid: $\text{HPO}_4^{2-}\text{(aq)}$; Conjugate base: $\text{H}_2\text{PO}_4^-\text{(aq)}$

Question 6

A student measures the solubility of silver chloride, $\text{AgCl}(s)$, in pure water. At $50^\circ\text{C}$, the solubility product constant, $K_{sp}$, for $\text{AgCl}(s)$ is $1.6 \times 10^{-9}$. What is the molar solubility of $\text{AgCl}(s)$ in pure water at $50^\circ\text{C}$?

Accepted Answer

$4.0 \times 10^{-5}\text{ M}$

Answer

$8.0 \times 10^{-5}\text{ M}$

Answer

$4.0 \times 10^{-4}\text{ M}$

Answer

$8.0 \times 10^{-4}\text{ M}$

Question 7

A student has two separate saturated aqueous solutions at equilibrium: Beaker 1 contains solid calcium carbonate, $\text{CaCO}_3\text{(s)}$, in contact with its ions, and Beaker 2 contains solid silver chloride, $\text{AgCl(s)}$, in contact with its ions. A few drops of concentrated nitric acid, $\text{HNO}_3\text{(aq)}$, are added to each beaker, significantly decreasing the pH of both solutions without noticeably changing the total volume. Which of the following predictions best describes the effect of decreasing the pH on the solubility of each solid?

Accepted Answer

The solubility of $\text{CaCO}_3\text{(s)}$ increases because $\text{CO}_3^{2-}\text{(aq)}$ reacts with $\text{H}^+\text{(aq)}$, whereas the solubility of $\text{AgCl(s)}$ remains unchanged because $\text{Cl}^-\text{(aq)}$ is the conjugate base of a strong acid.

Answer

The solubility of both $\text{CaCO}_3\text{(s)}$ and $\text{AgCl(s)}$ increases because $\text{H}^+\text{(aq)}$ reacts with the anions in both solutions to form weak acids.

Answer

The solubility of $\text{CaCO}_3\text{(s)}$ remains unchanged, whereas the solubility of $\text{AgCl(s)}$ increases because $\text{Ag}^+\text{(aq)}$ forms a soluble complex with nitrate ions.

Answer

The solubility of both $\text{CaCO}_3\text{(s)}$ and $\text{AgCl(s)}$ remains unchanged because $\text{H}^+\text{(aq)}$ does not react with metal cations in aqueous solution.

Question 8

A student investigates the reversible decomposition of phosgene gas, $\text{COCl}_2\text{(g)}$, in a sealed, rigid $1.0 \text{ L}$ flask according to the following equation: $\text{COCl}_2\text{(g)} \rightleftharpoons \text{CO(g)} + \text{Cl}_2\text{(g)}$ with $\Delta H^\circ = +108 \text{ kJ/mol}_{rxn}$. The system is allowed to reach equilibrium at $500 \text{ K}$. Which modification to the experimental procedure will increase the equilibrium yield of $\text{Cl}_2\text{(g)}$?

Accepted Answer

Increasing the temperature of the reaction vessel from $500 \text{ K}$ to $600 \text{ K}$

Answer

Adding a solid catalyst to the flask at $500 \text{ K}$

Answer

Decreasing the volume of the reaction container from $1.0 \text{ L}$ to $0.5 \text{ L}$ at $500 \text{ K}$

Answer

Injecting $0.10 \text{ mol}$ of $\text{Ar(g)}$ into the rigid flask at $500 \text{ K}$

Question 9

A student investigates the gas-phase synthesis of phosgene according to the following balanced equation:

$$ \text{CO}(g) + \text{Cl}_2(g) \rightleftharpoons \text{COCl}_2(g) $$

At $500 \text{ K}$, the equilibrium constant $K_c$ for the reaction is $5.0$. The student measures the initial concentrations of the gases in a rigid container at $500 \text{ K}$ and records the data in the table below.

| Species | Initial concentration (M) |
|---|---|
| $\text{CO}(g)$ | $0.10$ |
| $\text{Cl}_2(g)$ | $0.20$ |
| $\text{COCl}_2(g)$ | $0.30$ |

Which of the following correctly compares the reaction quotient, $Q_c$, to $K_c$ and describes the relative rates of the forward and reverse reactions immediately after mixing?

Accepted Answer

$Q_c = 15$; because $Q_c > K_c$, the rate of the reverse reaction is greater than the rate of the forward reaction.

Answer

$Q_c = 0.067$; because $Q_c < K_c$, the rate of the forward reaction is greater than the rate of the reverse reaction.

Answer

$Q_c = 15$; because $Q_c > K_c$, the rate of the forward reaction is greater than the rate of the reverse reaction.

Answer

$Q_c = 1.5$; because $Q_c < K_c$, the rate of the forward reaction is greater than the rate of the reverse reaction.

Question 10

A student investigates the solubility of three generic sparingly soluble salts in pure water at $25^\circ\text{C}$. The chemical formula and solubility product constant ($K_{sp}$) for each salt are provided in the table below.

| Salt | Formula | $K_{sp}$ at $25^\circ\text{C}$ |
|---|---|---|
| Salt 1 | $\text{MX}$ | $1.0 \times 10^{-10}$ |
| Salt 2 | $\text{QX}_2$ | $4.0 \times 10^{-12}$ |
| Salt 3 | $\text{ZX}$ | $1.0 \times 10^{-14}$ |

Which of the following correctly ranks the three salts in order of greatest to least molar solubility in pure water at $25^\circ\text{C}$?

Accepted Answer

$\text{Salt 2} > \text{Salt 1} > \text{Salt 3}$

Answer

$\text{Salt 1} > \text{Salt 2} > \text{Salt 3}$

Answer

$\text{Salt 1} > \text{Salt 3} > \text{Salt 2}$

Answer

$\text{Salt 3} > \text{Salt 1} > \text{Salt 2}$

Question 11

A student prepares a saturated solution of calcium fluoride, $\text{CaF}_2(s)$, at $25^\circ\text{C}$ and determines that the molar solubility of $\text{CaF}_2$ is $2.0 \times 10^{-4} \text{ M}$. Based on this measurement, what is the value of the solubility product constant, $K_{sp}$, for $\text{CaF}_2$ at $25^\circ\text{C}$?

Accepted Answer

$3.2 \times 10^{-11}$

Answer

$6.4 \times 10^{-11}$

Answer

$8.0 \times 10^{-8}$

Answer

$1.6 \times 10^{-7}$

Question 12

At $300 \text{ K}$, a chemical reaction has a standard Gibbs free energy change of $\Delta G^\circ = -10.0 \text{ kJ/mol}$. At this temperature, the product $RT$ is equal to $2.5 \text{ kJ/mol}$. Which of the following expressions is equal to the standard equilibrium constant, $K$, for the reaction at $300 \text{ K}$?

Accepted Answer

$e^{4}$

Answer

$e^{-4}$

Answer

$e^{0.25}$

Answer

$e^{10}$

Question 13

A student tests whether chloride ions in rinse water will form a precipitate when treated with silver ions. The student mixes equal volumes of $6.0 \times 10^{-5}\text{ M AgNO}_3$ and $6.0 \times 10^{-6}\text{ M NaCl}$ at $25^\circ\text{C}$. The volumes are assumed to be additive.

$\text{AgCl(s)} \rightleftharpoons \text{Ag}^+\text{(aq)}+\text{Cl}^-\text{(aq)}\qquad K_{sp}=1.8\times10^{-10}$

Which of the following correctly predicts whether a precipitate forms immediately after the solutions are mixed?

Accepted Answer

No precipitate forms because mixing equal volumes halves each ion concentration, giving \(Q_{sp}=9.0\times10^{-11}

Answer

A precipitate forms because \(Q_{sp}=9.0\times10^{-11}

Answer

A precipitate forms because $Q_{sp}=(6.0\times10^{-5})(6.0\times10^{-6})=3.6\times10^{-10}>K_{sp}$.

Answer

No precipitate forms because mixing equal volumes makes each ion concentration one-fourth its initial value, giving \(Q_{sp}=2.25\times10^{-11}

Question 14

A $1.0 \text{ L}$ rigid reaction vessel is filled with $1.0 \text{ mol}$ of $\text{NOCl}(g)$ at a fixed temperature. The reaction proceeds according to the equation below.

$$ 2\,\text{NOCl}(g) \rightleftharpoons 2\,\text{NO}(g) + \text{Cl}_2(g) $$

At this temperature, $K_c = 3.2 \times 10^{-8}$. Based on an ICE table and assuming that the change in concentration of $\text{NOCl}(g)$ is negligible, what is the equilibrium concentration of $\text{Cl}_2(g)$?

Accepted Answer

$2.0 \times 10^{-3} \text{ M}$

Answer

$4.0 \times 10^{-3} \text{ M}$

Answer

$6.0 \times 10^{-3} \text{ M}$

Answer

$8.0 \times 10^{-3} \text{ M}$

Question 15

A student models a high-temperature gas-processing system using a rigid container maintained at constant temperature. The gases react according to the equation

$2\text{SO}_3\text{(g)} \rightleftharpoons 2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)}$

Before appreciable reaction occurs, the partial pressures are $0.80\text{ atm}$ for $\text{SO}_3\text{(g)}$, $0.10\text{ atm}$ for $\text{O}_2\text{(g)}$, and $0\text{ atm}$ for $\text{SO}_2\text{(g)}$. At equilibrium, the total pressure in the container is $1.10\text{ atm}$. What is the equilibrium partial pressure of $\text{SO}_2\text{(g)}$?

Accepted Answer

$0.40\text{ atm}$

Answer

$0.10\text{ atm}$

Answer

$0.20\text{ atm}$

Answer

$0.30\text{ atm}$

Question 16

A rigid 1.0 L vessel contains an equilibrium mixture of $\text{X(g)}$ and $\text{Y(g)}$ according to the following balanced equation:

$\text{X(g)} \rightleftharpoons 2\text{Y(g)}$

At time $t_1$, additional $\text{Y(g)}$ is rapidly injected into the vessel at constant temperature. The concentration versus time graph for the system is shown below. Based on the graph, which statement correctly describes and explains the behavior of the system as it approaches a new equilibrium between $t_1$ and $t_2$?

Accepted Answer

The system shifts toward reactants because $Q > K_c$, with $[\text{Y}]$ decreasing by twice the amount that $[\text{X}]$ increases.

Answer

The system shifts toward products because the addition of $\text{Y(g)}$ increases the rate of the forward reaction, causing $[\text{X}]$ to decrease.

Answer

The system shifts toward reactants because $Q > K_c$, with $[\text{X}]$ increasing by twice the amount that $[\text{Y}]$ decreases.

Answer

The system shifts toward reactants because adding $\text{Y(g)}$ decreases the value of $K_c$, forcing the system to favor the reverse reaction.

Question 17

A student studies the gas-phase equilibrium used in sulfuric acid production.

$2\text{SO}_2\text{(g)}+\text{O}_2\text{(g)}\rightleftharpoons 2\text{SO}_3\text{(g)}$

After the system reaches equilibrium in a rigid vessel at constant temperature, the student injects inert $\text{Ar(g)}$. The total pressure increases, but the temperature and volume remain constant. Which statement correctly predicts and explains the effect of adding the $\text{Ar(g)}$ on the equilibrium position?

Accepted Answer

The equilibrium position does not shift because the partial pressure of each reacting gas remains unchanged, so $Q_p$ remains equal to $K_p$.

Answer

The equilibrium position does not shift because adding $\text{Ar(g)}$ increases the forward and reverse reaction rates by the same factor.

Answer

The equilibrium shifts toward $\text{SO}_3\text{(g)}$ because the increase in total pressure favors the side with fewer moles of gas.

Answer

The equilibrium shifts toward $\text{SO}_2\text{(g)}$ and $\text{O}_2\text{(g)}$ because adding $\text{Ar(g)}$ lowers the mole fractions and therefore the partial pressures of the reacting gases.

Question 18

A reaction system at $298 \text{ K}$ is represented by the balanced equation below.

$\text{2 NO}_2\text{(g)} \rightleftharpoons \text{N}_2\text{O}_4\text{(g)} \quad K_c = 2.0 \text{ at } 298 \text{ K}$

A student prepares a mixture of $\text{NO}_2\text{(g)}$ and $\text{N}_2\text{O}_4\text{(g)}$ in a rigid $1.0 \text{ L}$ container at $298 \text{ K}$, as represented in the particulate diagram. Each molecule in the diagram represents $1.0 \text{ mol}$ of that species. Which of the following best predicts how the system will respond to reach equilibrium?

Accepted Answer

The reaction will shift to the right to form more $\text{N}_2\text{O}_4\text{(g)}$ because $Q_c < K_c$.

Answer

The system is already at equilibrium because both $\text{NO}_2\text{(g)}$ and $\text{N}_2\text{O}_4\text{(g)}$ are present in the vessel.

Answer

The reaction will shift to the left to form more $\text{NO}_2\text{(g)}$ because $Q_c > K_c$.

Answer

The reaction will shift to the left to form more $\text{NO}_2\text{(g)}$ because the number of product molecules exceeds the number of reactant molecules.

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